Method for recovering hydrocarbons



. 0 Man IFIP'IMP;

XR 393U297l0 Feb. 7,1967 A. s. ODEH METHOD FOR RECOVERTNG HYDROCARBONS Filedfeb 1964 2 Sheets-Sheet 1 FIG.

I f v v AZIZ S. ODEH INVENTOR.

BY 6W ATTORNEY Filed Feb. 7, 1964 'Feb. 7, 1967' METHOD FOR RECOVERING HY DROCARBONS 2 Sheets-Sheet 2 FiG.3*

H 40 FEET H= 40 FEET h= 0.2 H

A212 5. ODEH INVENTOR.

ATTORNEY equal velocity through all the strata.

tinned States Parent 6 Filed Feb. 7, 1964, Ser. No. 343,280 6 Claims. (Cl. 1669) This invention relates to a method for recovering hydrocarbons from subterranean reservoirs. More particularly, it relates to such' method for recovering hydrocarbons from a formation or strata in fluid communication, over less than its thickness, with a wellbore.

In many situations in the production of hydrocarbons,

it is necessary to provide fluid communication between a wellbore and a strata of a hydrocarbon reservoir over less than the entire vertical thickness of such strata. For

example, the selective perforation of a casing in a wellbore over a distance less than the entire vertical interval of the strata it penetrates may be used to restrict the rate of fluid flow between the wellbore and such strata. Such arrangement may be utilized at the wellbore contact to each of .several adjacent strata having different fluid flowing characteristics to produce fluid flows at an More particularly, such partial perforations of a wellbore adjacent to each of several strata can be. utilized in various procedures employing injected or natural displacing fluid to assist in the optimum recovery of hydrocarbons. This arrangement is utilized to provide a more uniform movement ofthe fluids at the same velocity in each strata of the reservoir to secure a better recovery of hydrocarbons.

The nonuniform and unequal movement-of fluids in the various strata of the reservoir leads to tneflicient recovery of hydrocarbonsas a result of the bypassing of hydro! carbons in the reservoir by the displacing fluid. Additionally, such unequal movement of displacing fluid leads to. premature breakthrough of the. fluid into the wellbore. This fluid. may be of any type, such as carbon dioxide, natural gas, or water,.injected into, or resident in, the strata to assist in producing the hydrocarbons from the I reservoir.

Restricting fluid communication between a wellbore and an adjacent strata to less than its thickness has other useful applications. For example, it may be desirable not only to restrict the fluid flow. to a certain rate but to establish such flow only through a certain interval at the wellbore. One utility of such arrangement is to reduce water or gas coning. Another utility is to control the flow of a relatively high pressure fluid existing in such strata.

As will be apparent to those skilled in'the'art, the use ofsuch an interval of fluid communication at a wellbore creates problems in the Optimum production of. fluids from the adjacent strata. With the flow between the wellbore and strata through an interval of fluid communication, the flow potential distributions are of a spherical nature adjacent the interval of the wellbore and do not becomezradial until a substantial distance away from the wellbore in the formation. It is well known that with an interval of fluid communication extending from one horizontal boundary of the strata less than about 50 perinterval of fluid communication extends substantially ice through the entire thickness of the strata. Under these circumstances radial flow is obtained immediately adjacent the wellbore.

The distance through which fluids must flow through a selectively positioned interval of fluid communication between the wellbore and the strata before radial flow is established is one factor controlling the efliciency in the recovery of hydrocarbons from such strata. One reason for this result is that hydrocarbons in the strata where nonradial flow exists are bypassed and remain unproduced. Another reason for this result exists where a displacing or driving fluid used for displacing the hydrocarbons in the strata undergoes premature breakthroughs at areas of nonradial flow and thereafter more fluid is used to displace the hydrocarbons. Thus, the use of an interval of fluid communication to obtain a fluid flow between 21 wellbore and a given portion of a strata is well known. Similarly, it is known to restrict the fluid flow through such interval to obtain a desired rate of fluid flow therethrough. However, the problems relating to fluid flow through such interval-have not been solved.

It has been discovered that an interval of fluid com munication less than strata thickness can be placed at a desired position in a wellbore. relative to a strata for any given set of fluid flowing conditions therein to produce optimum flow conditions in the strata. More particularly, by using this discovery, the radial flow of fluid is ob tained under a given set of fluid flowing conditions in the strata as closely adjacent the wellbore as is possible with less than the entire strata thickness exposed for fluid communication to the wellbore. Of course, such discovery provides for optimum fluid flowing conditions in I such strata in the etfective production of hydrocarbons at the greatest efficiency.

It is therefore an object of the present invention to provide a method for recovering hydrocarbons under optimum fluid flowingconditions from reservoirs having strata exposed to fluid flow at a wellbore over an interval of'less than the thickness of such strata. Another object is to provide in such method-a definite relationship between the factors concerning fluid flow in a reservoir and the interval of fluid communication between a strata and wellbore so that the eflicient recovery of hydrocarbons may be obtained. Another object is to provide in such method for an interval of fluid communication less than the thickness of the strata at a position in a wellbore where radial flow is obtained in the strata more closely adjacent the wellbore than has heretofore been obtained. Another object is to provide for the utilization of at least one positioned interval of fluid communication in a well bore adjacent to each strata with the fluid flow restricted through some of the intervals such that optimum fluid flowing conditions are obtained through the uniform and aligned movement of fluids in each of the strata for the maximum recovery of hydrocarbons from each such strata. Another object is to provide for the recovery of hydrocarbons from a reservoir in accordance with the preceding objects where all factors concerning the flow of fluid in each strata in the reservoir have a definite relationship and which relationship may be correlated to any particular strata and any set of fluid flowing conditions encountered in the production of hydrocarbons in a steady state flow.

These and'other objects will be readily apparent from the following description of the present invention when taken in reference to the appended claims and the attached drawings, wherein:

FIGURE 1 is a vertical section through a reservoir in the earth containing hydrocarbons in which the method of this invention can be practiced;

FIGURE 2' is a partial view of the reservoir shown in FIGURE 1 to illustrate one application of the method of a wellbore over an interval less than its total thickness;

and which interval is located at a certain intermediate position in the strata in order that, for a given flow of fluid through such interval between the wellbore and the strata responsive to a given velocity potential, radial flow is produced in the strata more closely adjacent to the wellbore than at any other arrangement where complete radial flow does not exist by the step of producing hydrocarbons in a definite relationship; a specific definition of which will be fully presented hereinafter, to the fluid flowing conditions in the reservoir.

In one aspect, the present invention is a method for producing hydrocarbons from a production well by obtaining maximum invasion efliciency at breakthrough of an injection fluid which is passed from an adjacent injection well into an intervening stratified reservoir. In-

vasion efliciency may be defined as the hydrocarbon pore space invaded, or contacted, by the injected fluid or each hundred units of hydrocarbon pore space enclosed by the injection fluid, through the full reservoir thickness, at the leading edge of the injection front. Maximum invasion er nciency at breakthrough is obtained where the injection fluid front advances at the same rate through all of the 'stratified reservoir.

Referring to FIGURE 1, a reservoir is shown as penetrated by an injection well 11 and by a production well 12. The reservoir 10 is comprised of dissimilar oilbearing sands 13 and 14. The injected fluid is water, but

other fluids may be used, if desired. In this description it will be assumed that the sands 13 and 14 are horizontally enclosed by an impervious overburden 15 and supporting strata 16. It is further assumed that the sand 44 has such characteristics as to limit a water injection front rate of advance, for the same injection conditions, below that obtainable in the sand 13. The well 11, provided with means for injecting water, is completed throughout the sand 14 and the well 12, provided with means for producing hydrocarbons, is completed throughout both the sands 13 and 14.

The sands 13 and 14 can be assumed to have the following properties:

Sand 13 Sand 14 Permeability, md s 500 200 Pnrosity. 0,18 0.18 Thickness, it 40 30 Residual Oil Saturation. porcent 3t) 32 Original Water Saturation, percent 2O The sands 13 and 14 in the reservoir 10 have difierent physical characteristics, such as thickness and permeability; and, therefore, the. rates of water injection, at the same driving pressure into the sands 13 and 14 of the reservoir 10, will be dissimilar. The water injection front will have a rate of advance in the sand 13 greater than in the sand 14. Thus, the water injected throughout the vertical interval of the sand 13 will break through into the flowof significant merit occurs vertically between the sands 13 and 14 of the reservoir 10 and the conditions of fluid injection are in a steady state.

The velocity potential Aqa which drives the waterflood through the reservoir 10 is the difference between the velocity potentials at the injection well 11, and production well 12, Le, A,,. The injection rate, q in the sand 14 for radial flow is defined by the equation:

wherein:

The injection rate per unit thickness V is defined by the equation:

Thus, the rate of injection front advance R is defined the equation:

(Porosity) l original water saturationresidual oil saturation) In the sand 14 with the whole interval of strata receiving i the injection of fluid from the well 11, the rate of injection front advance R is defined by the equation:

R: V 21M 21k Ap 0.18XOA8 0.08641 r 0.0864 in r In the same manner, the rate of injection front advance R in the sand 13 with the whole interval of strata receiving the injection of fluid from the well 11 is defined by the equation:

wherein the terms were previously defined with respect to the Equation 1 but having the numerical values of the physical characteristics of the sand 13.

If both the sand 13 and 14 were open throughout their entire intervals to the well 11, the ratio of the injection front advances between the sand 13 and 14 under the same injection pressure would be defined by the equation:

2rr(500)Ap o 0.09 1. In 7 R Equation '1 21r(2O0)Ap 0.0864 In r (6) Thus, the injection front would advance at a rate 2.4 times as fast in the sand 13 as in the sand 14. Severe premature breakthrough of the injected fluid would occur in the sand 13.

Obviously, to obtain the same rate of injection frontadvance in both sands 13and 14, the sand 13 is not open throughout its interval at the well 11 to fluid commnnication. The sand 13 is only opened to fluid communication over an interval to the extent required to limit the full interval rate of flow q to be reduced by a factor of 2.4. Thus, the desired restricted rate of flow q, i.e.. the injec- R Eqnation 5 tion rate; into the sand 13 is q/q,=l/2.4=0.42. Simply water.

7 rate of flow q, to 42 percent of its value is obtained by an interval of fluid communication less than the thickness of the sand 13 at the well 11. This arrangement is necessary to make the injection front advance in the sands 13 and 14 at the same velocity. One means to obtain'such restricted injection or flow rate q of water from the well 11 into the sand 13 is by exposing to the well 11 only an interval of the sand 13 to fluid communication. Where-a casing is cemented within the well 11,. the use of. perforations toestablish fluid communication between the well 11' and adjacent strata may be uti- .procedures disclosed in the United States Letters Patents 2,352,834 and'2,973,039;

Where a fluid is injected into a strata-like sand 13 through an area less than the total strata interval and such area is not correctly positioned adjacent the strata, several undesired results can be produced. One result is that the injected fluid may travel as spherical flow for a substantial distance from the injection well 11 before becoming radial flow.- This will cause some area of. the sand 13 to be bypassed by the injected fluid. Another result is that a considerable vertical misalignment of the injection fronts can occur before the flood front of inwherein:

P is the pressure,

p is the density of water,

k is the permeability of the sand 13 to water, g is the acceleration of gravity, and

p. is the viscosity of the injected water.

Equation 7 is to be solved for the boundary conditions:

(a) the potential at the production well 12, i.e., at r=r and (b) q=-21rhr6/6rl, where q is the rate of fluid injection which is constant, and V (c) 6/6z=0 at 2:0 and H.

The boundary conditions (a) and (b) are that the potential is constant at the producing well, and the fluid injection is at a constant rate, respectively; and the boundary condition (c) is the requirement that no fluid passes vertically across the horizontal boundaries of the sand 13.

If it is recalled that A -4 for injection in the well 11', thenEquation 7 as applied thereto resolves to the equation:

. a a s/ar -1sA/rar+s /az =0 (9) The Equation 9'is readily solved by the finite cosine transform:

H A= I ma cos azdz, wherein a =n1r/H After transforming and performing the usual algebraic steps, the Equation 9 solution for the before-mentioned boundary conditions is obtained as the equation:

jection water in the sand 13 is stabilized at substantially a constant rate, the same as in the sand 14. This will produce a premature arrival of the injection front of water from the sand 13 into the well 12 before arrival from the sand 14. For example, placing the interval or opening for injecting fluid from thewell 11 at the top, or bottom, of the sand 13 will produce a fluid flowing condition the same as obtained by partially penetrating wells in similar-isotropic formations. Reference may be had to the text "Physical Principles of Oil Production by Muskat, edition of 1949, at pages 205 to 219, inclusive,

. for'examples of such fluid flowing conditions.

It is the purpose of the present method to place the interval of fluid communication to the sand 13 at a location in the well 11 spaced from the horizontal boundaries of the sand 13 andralso specifically-positioned therein where the priorly mentioned undesired results are minimized and the invasion efficiency is maximized. Referring now to FIGURE 2, the sand 13 and the well 11 are shown in detail with an interval 11 of fluid communication to provide the flow rate ratio, q=0.42q of the injected The sand 13 is of thickness H adjacent the well 11. The interval -'h is spaced from the horizontal boundaries of the sand 13". The interval h is positioned in the well 11 spaced at a distance z from one horizontal boundv ary, such as the top, of the sand 13.

The pressure in a steady state flow does not vary with time at any one point in the sand 13. if the potential is s at any distance r from thewell 11 with the mobility ratio of 1:1, then for steady state flow, is described by p the following equation:

: As is apparent, 4:, the velocity potential, is defined by the equation:

I F m-m) (8) wherein.R;,=r /H, R =r /H, y=z/H, and i=h/H.

Those skilled in the art will recognize that the latter portion of the Equation 10 contains Bessel Functions which include modified BesselFunctions of the first kind, zero order, modified Bessel Functions of the second kind, zero order, modified Bessel Functions of the first kind, first order and modified Bessel Functions of the second kind, first order. The general definition y=z/H is fractional as to the position of the interval h. The term z is a coordinate defining the distance from one horizontal boundary of the sand 13 to one horizontal boundary of the interval h. The coordinates z and 2 then mathematically define the top and bottom boundaries of the interval h. Substitution of these coordinates into the general definition y=z/H provides:

The y and y are then particular expressions for defining the specific locations of the top and bottom of the interval h in the sand 13' as mathematically derived from the general definition y=z/H.

In practicing the method of this invention, Equation 10 defines the relationship between the fluid flowing conditions providing for the optimum production of hydrocarbons from the sand 13 and the sand 14.

For example, with the sands 13 and 14 open to flow throughout their thicknesses at the well 11, the Equation 10 becomesreduced to the equation:

Thus, for a certain velocity potential mp, the rates of flow q from the well 11 into each of the sands 13 and 14 can be calculated. Therefore, for the same A the ratio of these rates of flow becomes an index to the necessary restriction of flow to provide the restricted rate of flow q into the sand 13 from the well 11. Usually, the ratio determined from FIGURE :15 at page 218 in the cited reference to Muskat.

With reference to Equation 10, it is clearly seen that there is adefinite relationship for any strata between q and A 5 in respect to F, y, z, and H. Returning to our specific example of the sands 13 and 14, the relationship of these terms in the method of this invention is as follows. A finite solution of the Equation by applying the terms H=40 feet and q/q,=0.42 with well 11 assumed as having a radius of .25 foot (r and spaced from well 12 a distance of 660 feet (r (the usual arrangement of well spacing) provides that the interval h extends 0.2 of the thickness, or 8 feet, of the sand 13 and that the top of the interval h is positioned 0.15 of the thickness or a z of 6 feet, in the sand 13 below its upper horizontal boundary.

Although the Equation 10 can be solved manually withthe above fluid flowing conditions through the use of the Tables of Vessel Functions, a better method is by the use of a computer, such as the Control Data Corporation Model i604 for performing the desired solutions.

A suitable .graphic display may also be prepared to provide a visual record of the solution of Equation 10 to simplify its future applications to a variety of reservoir conditions since r and r are the most common well parameters encountered. For this purpose with a certain Alp, Equations 10 and 11 were subject to computation to provide the rates of flow from each of the sands 13 and 14 over their entire thickness. The ratio of these flow rates is the index to restriction of flow of fluid previously mentioned for the sand 13, i.e., q/q at the up. For each ratio of q/q the interval 11 and y=z/H were determined by holding all but one of the terms constant and comput ing the remainingierm with r and r being assumed as 660 feet and .25 foot, respectively. In FIGURES 3, 4, and 5 are graphic illustrations of these computed terms it and y where for each strata thickness H of 40 feet, for a given interval h of integer tenths of H, 0.1H, 02H and 0.3I-I, positioned at a distance y from one horizontal boundary of the sand 13, there is a finite value of q/q Similar curves can be determined for other perforated intervals h and other sand thickness H.

The curves of FIGURES 3, 4, and 5 can be used for any strata 40 feet in thickness to provide the magnitude of the interval h of fluid communication at the sand 13 exposed to the well 11 and its position 2 from the top of the sand 13, both of which were previously computed from the Equation 10 where r and r are reasonably similar to the stated values. Where H=40 feet and q/q =0.42, reference to the FIGURES 3, 4, and 5 shows that only the curve of FIGURE 4 yields a solution. With particular reference to FIGURE 4, it is seen that for a q/q,==0.42 that the interval h is 02H and its position 2 is 0.15 of the thickness H of the sand 13 from its top horizontal boundary. Obviously, prior computation of the curves like that of FIGURES 3, 4, and 5 for varied strata thickness and well spacings simplifies and expedites the solution to the problem of determining the perforated interval h and its location z adjacent the sand 13 in the well 11.

1 is substantially aligned along the vertical in both the sands 13 and 14. These conditions are most apparent to pro- 8 duce the optimum production and recovery of petroleum from the well 12.

Another aspect of the method of this invention is the application of Equation 10 to the production of reservoir fluids from the sands 13 and 14 into the well 11 responsive to an artificial or natural water drive under asteady state from the region of the well 12. The water drive should advance at a constant rate through the reservoir 10 to the well 11. The method is applied in the same manner as for water injection at the well 11 with i.e., the velocity potential A driving hydrocarbons into the sand 13 adjacent the well 11 on the production of fluids into the well 11 through the perforated interval h can be readily determined. For this determination, assume the previously defined dimensions, H=40 feet, 11:8 feet, 2:6 feet, and the ratio of rates of flow, q/ 1],, through the interval h to the entire strata to be 0.42, etc. For example, from the Equation 11, the potential flow rate of reservoir fluids, q through the entire sand 13 into the well is determined. By calculations from the Equation 10, the optimum flow rate of reservoir fluids, q, through the interval h at a position 2 into the well 11 from the sand 13 is determined. Experimental measurement is made of the actual rate of flow of reservoir fluids, q, into the well 11 from the sand 13 through the interval 11. Comparison of the measured and calculated rates of flow will clearly show the existence and magnitude of any mud damage to the sand 13 adjacent to the well 11. Thus, expensive and sometimes harmful acidizing, fracturing, and similar remedial measures are found unnecessary where the restricted flow rate q isa result of using an excessively small interval it. Even if such remedial remedies were applied, they may not improve the production of reservoir fluids through the interval h since they would not solve the basic problem. Obviously, under such condition adequate remedy by this invention resides Y in providing a lengthened interval h of fluid communication as a method of well completion and producing petroleum by this method as defined by Equation 10. Where mud damage, or other formation defects, restricts the production of petroleum through an adequate interval h, acidizing, fracturing, and the like would be proper, followed by producing petroleum by this method as defined by Equation 10.

It will be apparent that by the method of this invention fluid flow between the well 11 and the sand 14 may be through only an interval of fluid communication less than its thickness. Thus, in a plurality of strata forming a hydrocarbon reservoir, all, or only some, of the strata may employ the interval of fluid communication applied in accordance with the Equation 10.

From the foregoing, it will be apparent that there has been provided herein a novel method for producing hydrocarbons from subterranean reservoirs under optimum fluid flowing conditions. Further, these objects are accomplished through the use of a method in which optimum fluid flowing conditions are obtained by having these conditions arranged in a definite relationship so as to obtain the eflicient recovery of hydrocarbons. Although it will be apparent to those skilled in the art to make various changes to the method of this invention without departing from its scope to conform to certain situations, it is intended that these changes, other alterations, and

related variations are considered as part of the present invention and within the scope of the appended claims. It is further intended that the foregoing description is to be taken. as a means of illustration and not as a means of limitation. The only limitations to be applied to this invention are in the following claims.

What is claimedis:

- 1. A method for the production of hydrocarbons by obtaining optimum fluid flowing conditions in a reservoir having a strata of thickness H penetrated by a wellbore of radius r which wellbore is in fluid communication with the strata over an interval of height h with said interval disposed at a distance zfrom pne horizontal boundary of Y the strata responsive to a differential velocity potential A existing in the strata between the wellbore and a radial boundary r of the-strata comprising the steps of:

(a) .flowing'fluids at a fluid flow rate q through the (a) flowing fluid between the wellbore and one of the strata at a given magnitude of velocity of fluid flow flow as mentioned in said one of the strata in each of the other strata by restricting the fluid flow to an interval h in the wellbore between the wellbore and each such other strata with the interval positioned at a distance 2 from a horizontal boundary in each such other strata in the relationship:

interval between the wellbore and the strata in the relationship:

wherein R =r /H, R =r /H, y=z/H, y and y; are particular expressions, of the general expression wherein R =r /H, R =r /H, y=z/H, y and y are particular expressions, of the general expression y=z/H, for the specific coordinate locations of the top and bottom of said interval, 7i=h/H, and

(b) producing hydrocarbons by such flowing fluids until substantial quantities of the hydrocarbons are recovered from the reservoir, 7

2. A method for the production of hydrocarbons by obtaining optimum fluid flowing conditions in a reservoir v having 'a strata of thickness H penetrated by a wellbore of radius r which wellbore is in fluid communication with the strata through an interval of height h with said interval positioned at a distance z from one horizontal boundary ofthe strata and where a diflerential velocity potential A exists between the wellbore and a radial boundary of the strata to provide a fluid flow rate q" through the interval by the steps comprising:

(a) completing the wellbore in the relationship: 7

y=z/H, for the specific coordinate locations of the top and bottom of said interval, 'fi=h/H, and (c) producing hydrocarbons from the strata by such flowing fluid at the same magnitude of velocity of fluid flow in all the strata until substantial quantities of hydrocarbons are recovered from the reservoir between the wellbore and the radial boundary r 4. A method for the production of hydrocarbons through a wellbore penetrating a reservoir having at least two strata of different fluid flowing characteristics by the steps comprising:

(a) injecting a driving fluid from a first wellbore with a radius r into one of the strata at a velocity potential 4 to establish a given velocity of the driving fluid front advance toward a second wellbore spaced from the first wellbore a radial distance r and producing hydrocarbons displaced by the driving fluid into the second wellbore at a velocity potential the dilferential velocity potential A 5 is ga -p between the wellbores to move fluids through the strata,

(b) injecting the driving fluid from the first wellbore into each of the other strata at a limited flow rate q to obtain the same velocity of driving fluid front advance toward the second wellbore in each of the other strata responsive to the velocity potential A45 by restricting the fluid flow to an interval h in the first wellbore at each such other strata of thickness H with the interval positioned at a distance z from a horizontal boundary in each such other strata in the relationship:

11 wherein R =r /H, R ==r /H, y=z/H, y, and y: are particular expressions, of the general expression y=z/H, for the specific coordinate locations of the top and bottom of said interval, 7i=h/H, and (c) producing hydrocarbons from the strata through the second wellbore by continuing the injecting of driving fluid from the first wellbore into each of the strata to advance the driving fluid front at a constant velocity of fluid flow in each of said strata until substantial quantities of hydrocarbons are recovered from the strata of the reservoir between the first and second wellbores. i 5. A method for the production of hydrocarbons through a wellbore penetrating a reservoir having at least two strata of diflerent fluid flowing characteristics by the steps comprising:

(a) passing a driving fluid front through the strata of the reservoir toward a wellbore with a radius r to produce hydrocarbons at a velocity potential into the wellbore, the driving fluid front initiallylocated in the strata at a radial distance r from the wellbore and having a velocity potential 45 at such initial location, the differential velocity potential A advancing said driving fluid front is (b) producing hydrocarbons from each of the strata containing the driving fluid front into the wellbore, the produced fluids from the strata restricted to a rate of fluid flow q into the wellbore to obtain a constant velocity of driving fluid front advance equal to the advance through one of the strata responsive to the dillerential velocity potential Ad, the-production of hydrocarbons through an interval 11 in the wellbore at such strata of thickness H where an adjusted rate ot'flow-is provided with the interval posi- 12 tioned at a distance 2 from one horizontal boundary of each such strata in the relationship:

wherein R r /H, R =r /H, y=z/H, 3 and y; are particular expressions, of the general expression 10 y= /H, for the specific coordinate locations of the top and bottom of said interval, li=h/H,- and (c) producing hydrocarbons from the strata through the wellbore responsive to the driving fluid front ad- 15 vancing at the same velocity in each strata until substantial quantities of hydrocarbons are recovered from the reservoir. i 6 A method for the production of hydrocarbons through a wellbore penetrating a reservoir having at least 20 two strata of different fluid flowing characteristics by the steps comprising:

(a) flowing hydrocarbons from the wellbore of radius r from each of the strata of thickness H at individual rates of flow q by exposing the wellbore at each strata to fluid flow for an interval h disposed a distance z from one horizontal boundary of each such strata, the fluid flow being responsive to a differential velocity potential Aq') present between the wellbore and a radial boundary r in the reservoir, each rate of flow q for each strata having a magnitude that the velocity of fluid flow in the strata is the same and in each strata for each rate of flow q the terms h, z, and y have the relationship:

ervoir through the wellbore.

References Cited by the Examiner OTHER REFERENCES Muskat, Physical Principles of Oil Production, 1st edition, McGraw-Hill Book Co. Inc, 1949, New

205-210 and 259 to 266.

York, pages ERNEST R. PURSER, Primary Examiner.

4 CHARLES E. OCONNELL, Examiner.

S. I. NOVOSAD, Assistant Examiner.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3, 302 710 February 7 1967 Aziz S. Odeh It is hereby certified that error appears in the above numbered patent requiring correction and that the said Letters Patent should read as corrected below.

Column 3 l ine 4 2, for "44" read 14 column 4 line 7 for "g -A read Q1 ff line 29, before "the" insert by column 10 line 9 after "the" second occurrence insert other line 10 after "thickness" insert H Signed and sealed this 10th day of October 1967.

(SEAL) Altcst:

EDWARD J. BRENNER Edward M. Fletcher, Jr.

Commissioner of Patents Attcating Officer 

1. A METHOD FOR THE PRODUCTION OF HYDROCARBONS BY OBTAINING OPTIMUM FLUID FLOWING CONDITIONS IN A RESERVOIR HAVING A STRATA OF THICKNESS H PENETRATED BY A WELLBORE OF RADIUS RW, WHICH WELLBORE IS IN FLUID COMMUNICATION WITH THE STRATA OVER AN INTERVAL OF HEIGHT H WITH SAID INTERVAL DISPOSED AT A DISTANCE Z FROM ONE HORIZONTAL BOUNDARY OF THE STRATA RESPONSIVE TO A DIFFERENTIAL VELOCITY POTENTIAL 